Rayleigh collapse

In Fig. 1.4a, an example of the radius-time curve for a stably pulsating bubble calculated by the modified Keller equation is shown for one acoustic cycle [43]. After the bubble expansion during the rarefaction phase of ultrasound, a bubble strongly collapses, which is the inertial or Rayleigh collapse. After the collapse, there is a bouncing radial motion of a bubble. In Fig. 1.4b, the calculated flux of OH... 

In acoustic cavitation, some bubbles dramatically expand and violently collapse, which is called the inertial collapse or Rayleigh collapse. It is caused by both the spherically shrinking geometry and the inertia of the surrounding liquid which inwardly flows into the bubble. The bubble collapse is similar to that in hydrodynamic cavitation which is induced by a sudden drop of pressure below the saturated vapor pressure due to a fluid flow through an orifice [92, 93]. At the end of the... 

Figure 22 - (left) Idealized elongated bubble with different wall curvatures (right) Rayleigh collapse curves of spherical bubbles with radii rmin cmd r ax... 

Quiben JM, Thome JR (2007b) Flow pattern based two-phase pressure drop model for horizontal tubes. Part II. New phenomenological model. Int. J. Heat and Fluid Flow. 28(5) 1060-1072 Rayleigh JWS (1917) On the pressure developed in a liquid during the collapse of a spherical cavity. Phil Mag 34 94-98... 

One solution that was considered by Rayleigh (Lamb, 1945) for the determination of bubble collapse time, tm, used the model of a bubble with initial size Rm, suddenly subjected to a constant excess liquid pressure pL. Neglecting the surface tension and the gas pressure in the bubble, Eq. (2-29) may be rearranged to... 

Now the bubble collapse is discussed using the Rayleigh-Plesset equation. After the bubble expansion, a bubble collapses. During the bubble collapse, important terms in the Rayleigh-Plesset equation are the two terms in the left hand side of (1.13). Then, the bubble wall acceleration is expressed as follows. 

Rayleigh L (1917) On the pressure developed in a liquid during the collapse of a spherical cavity. Philanthropic Mag 34 94-98... 

The important break through in the understanding of cavitation came in 1917 when Lord Rayleigh [12] published his paper On the pressure developed in a liquid during the collapse of a spherical cavity . By considering the total collapse of an empty void under the action of a constant ambient pressure Pq, Rayleigh deduced both the cavity collapse time t, and the pressure P in the liquid at some distance R from the cavity to be respectively (Eqs.2.25 and 2.26). 

Fig. 2.14. Pressure developed in a liquid surrounding a collapse Rayleigh cavity Z = volume compression ratio.

U nlike Rayleigh s original example of a collapsing empty cavity, this bubble will reduce to a minimum size, on compression, after which it will expand to Rj and subsequently it will oscillate between the two extremes R and Rf in. Obviously at the two extremes of radii, motion of the bubble wall is zero - i. e. R = 0. To determine these radii it is necessary to integrate Eq. A.25. With Z = (R /R), the integration yields ... 

A neutral collapsed polymer chain can be considered in a first approximation as a liquid drop which undergoes the Rayleigh instability when it becomes charged [64, 66]. The various daughter drops are however linked into a chain and the daughter drops cannot separate from each other. They remain linked by stretched polymer strands. The picture that is obtained for a polymer chain in a poor solvent is thus that of a necklace of collapsed globules, the pearls, connected by the strands that are stretched by the electrostatic interactions between the pearls. 

The pearls are just at the Rayleigh instability threshold, their density is that of a collapsed globule and their size is obtained from the Rayleigh charge. It is the so-called electrostatic blob size... 

Figure 12. Lagrangian path lines at various stages of a Rayleigh-Taylor collapse for the case of two inviscid, incompressible fluids having a density ratio of 2 1. A free surface is present above the dense fluid and the interface between the fluids is indicated for each stage. The simulation shows how later evolution of the fluid flow is dominated by the strength and dynamics of the vortex pair created during the...

Fig. 14.2. Principle of filamentation. The beam first self-focuses and collapses due to the Kerr effect. Ionization at the non-linear focus then defocuses the beam. A dynamical balance establishes between both processes over distances much over the Rayleigh length...

Instead, sonochemistry and sonoluminescence derive principally from acoustic cavitation, which serves as an effective means of concentrating the diffuse energy of sound. Compression of a gas generates heat. When the compression of bubbles occurs during cavitation, it is more rapid than thermal transport, which generates a short-lived, localized hot-spot. Rayleigh s early descriptions of a mathematical model for the collapse of cavities in incompressible liquids predicted enormous local temperatures and pressures.13 Ten years later, Richards and Loomis reported the first chemical and biological effects of ultrasound.14... 

The relatively mild growth and the violent collapse processes predicted by the asymptotic forms (4-210) and (4-211) are characteristic of the dynamics obtained by more general numerical studies of the Rayleigh-Plesset equation, but additional results for cases of large volume change are not possible by analytic solution. In the remainder of this section, we consider additional results that can be obtained by asymptotic methods. 

---